Question

Determine the zeroes of the polynomial p(x) = x3 – 2x2

. Also verify the relationship

between the zeroes and the coefficient.

​

Answer 1

The zeroes of the polynomial are 0, 0, 2

Step-by-step explanation:

Given:

The polynomial

$p(x)=x^3-2x^2$

To find out:

The zeroes of the polynomial and verify the relationship between the zeroes and coefficient

Solution:

The given polynomial

$p(x)=x^3-2x^2$   ............ (1)

Since this is a cubic polynomial, there will be 3 zeroes

To determine the zeroes of the polynomial

$p(x)=0$

$\implies x^3-2x^2=0$

$\implies x^2(x-2)=0$

$\implies x=0,0,2$

The zeroes of the polynomial are 0,0,2

Comparing the polynomial (1) with general cubic polynomial

$p(x)=ax^3+bx^2+cx+d$

We get

a = 1

b = -2

c = 0

d = 0

Here,

Sum of the zeroes = 0 + 0 + 2 = 2

And -b/a = -(-2/1) = 2

Thus, it is verified that

Sum of the zeroes = -b/a

Sum of zeroes taken two at a time = 0×0 + 0×2+2×0 = 0

And c/a = 0/1 = 0

Thus, it is verified that

Sum of zeroes taken two at a time = c/a

Sum of zeroes taken three at a time = 0×0×2 = 0

And -d/a = -0/1 = 0

Thus, it is verified that

Sum of zeroes taken three at a time = -d/a

Hope this answer is helpful.

Know More:

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Answer 2

Answer:

Step-by-step explanation: